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Question Number 62945 Answers: 1 Comments: 0

Find the greatest coefficient in the expansion of (6 − 4x)^(−3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\:\:\left(\mathrm{6}\:−\:\mathrm{4x}\right)^{−\mathrm{3}} \\ $$

Question Number 62942 Answers: 1 Comments: 10

Make r the subject of the formular: S = ((a(r^n − 1))/(r − 1))

$$\mathrm{Make}\:\:\mathrm{r}\:\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{S}\:\:=\:\:\frac{\mathrm{a}\left(\mathrm{r}^{\mathrm{n}} \:−\:\mathrm{1}\right)}{\mathrm{r}\:−\:\mathrm{1}} \\ $$

Question Number 62938 Answers: 1 Comments: 1

Question Number 62937 Answers: 1 Comments: 3

∫_0 ^( x) (1/(1+x^2 )) dx

$$\int_{\mathrm{0}} ^{\:\:\mathrm{x}} \frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 62930 Answers: 0 Comments: 0

find the value ∫_0 ^1 x^(√x) dx (study first the convergence)

$${find}\:{the}\:{value}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{x}^{\sqrt{{x}}} {dx}\:\left({study}\:{first}\:{the}\:{convergence}\right) \\ $$

Question Number 62925 Answers: 1 Comments: 0

Three friends , Boakye , kwame and kojo thinking that they are decieving their parents decided to take turns to run away from their parent . Boakye run away on monday of the first week. After how many weeks will he run again on monday?

$$\mathrm{Three}\:\mathrm{friends}\:,\:\mathrm{Boakye}\:,\:\mathrm{kwame}\:\mathrm{and}\: \\ $$$$\mathrm{kojo}\:\mathrm{thinking}\:\mathrm{that}\:\mathrm{they}\:\mathrm{are}\:\mathrm{decieving}\: \\ $$$$\mathrm{their}\:\mathrm{parents}\:\mathrm{decided}\:\mathrm{to}\:\mathrm{take}\:\mathrm{turns}\:\mathrm{to}\: \\ $$$$\mathrm{run}\:\mathrm{away}\:\mathrm{from}\:\mathrm{their}\:\mathrm{parent}\:. \\ $$$$\mathrm{Boakye}\:\mathrm{run}\:\mathrm{away}\:\mathrm{on}\:\mathrm{monday}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{week}.\:\mathrm{After}\:\mathrm{how}\:\mathrm{many}\:\:\mathrm{weeks}\:\mathrm{will}\: \\ $$$$\mathrm{he}\:\mathrm{run}\:\mathrm{again}\:\mathrm{on}\:\mathrm{monday}? \\ $$

Question Number 62924 Answers: 1 Comments: 2

find min_((a,b)∈R^2 ) ∫_(−1) ^1 (ax+b)^2 dx

$${find}\:{min}_{\left({a},{b}\right)\in{R}^{\mathrm{2}} } \:\:\:\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \left({ax}+{b}\right)^{\mathrm{2}} {dx} \\ $$

Question Number 62919 Answers: 0 Comments: 1

kelvin and price were contesting for an election in the year 2016, kelvin lost the election and prince won the election thursday of the second week of December. After how many days will prince win the election again on thursday if the eletion is postponed to the first week of january. suppose (kelvin continious to loose the eletion again in the next four years to come). please help me solve this quetion

$$\mathrm{kelvin}\:\mathrm{and}\:\mathrm{price}\:\mathrm{were}\:\mathrm{contesting}\:\mathrm{for}\:\mathrm{an} \\ $$$$\mathrm{election}\:\mathrm{in}\:\mathrm{the}\:\mathrm{year}\:\mathrm{2016},\:\mathrm{kelvin}\:\mathrm{lost}\:\mathrm{the} \\ $$$$\mathrm{election}\:\mathrm{and}\:\:\mathrm{prince}\:\mathrm{won}\:\mathrm{the}\:\mathrm{election}\:\mathrm{thursday} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{second}\:\mathrm{week}\:\mathrm{of}\:\mathrm{December}.\:\mathrm{After} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{prince}\:\mathrm{win}\:\mathrm{the}\:\mathrm{election} \\ $$$$\mathrm{again}\:\mathrm{on}\:\mathrm{thursday}\:\mathrm{if}\:\mathrm{the}\:\mathrm{eletion}\:\mathrm{is}\:\mathrm{postponed}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{week}\:\mathrm{of}\:\mathrm{january}.\:\mathrm{suppose}\:\left(\mathrm{kelvin}\:\mathrm{continious}\right. \\ $$$$\mathrm{to}\:\mathrm{loose}\:\mathrm{the}\:\mathrm{eletion}\:\mathrm{again}\:\mathrm{in}\:\mathrm{the}\:\mathrm{next}\:\mathrm{four} \\ $$$$\left.\mathrm{years}\:\mathrm{to}\:\mathrm{come}\right).\: \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{quetion} \\ $$

Question Number 62914 Answers: 1 Comments: 0

Question Number 62912 Answers: 1 Comments: 0

Question Number 62962 Answers: 0 Comments: 0

P(x)=tan^(−1) (x)=Σ_(n=0) ^∞ (((−1)^n x^(2n+1) )/(2n+1)) P_(1000) (x)=? what is this sum in terms of x?

$${P}\left({x}\right)=\mathrm{tan}^{−\mathrm{1}} \left({x}\right)=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {x}^{\mathrm{2}{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{1}}\: \\ $$$${P}_{\mathrm{1000}} \left({x}\right)=?\:{what}\:{is}\:{this}\:{sum}\:{in}\:{terms}\:{of}\:{x}? \\ $$

Question Number 62908 Answers: 0 Comments: 1

∫((arctan(x))/x)dx

$$\int\frac{{arctan}\left({x}\right)}{{x}}{dx} \\ $$

Question Number 62907 Answers: 1 Comments: 1

∫(√(((1+x)/(1−x)) ))(1+x) dx

$$\int\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\:}\left(\mathrm{1}+{x}\right)\:{dx} \\ $$

Question Number 62923 Answers: 2 Comments: 0

Question Number 62906 Answers: 0 Comments: 3

∫x^x dx

$$\int\mathrm{x}^{\mathrm{x}} \mathrm{dx} \\ $$

Question Number 62895 Answers: 1 Comments: 2

Question Number 62885 Answers: 0 Comments: 0

Question Number 62889 Answers: 1 Comments: 0

Question Number 62882 Answers: 0 Comments: 3

let f(x)=ln∣((x−1)/(x+1))∣ 1)determine D_f 2) calculatef^((n)) (x) and f^((n)) (0) 3) developp f at integr serie 4) calculate ∫_(−(1/2)) ^(1/2) f(x)dx .

$${let}\:{f}\left({x}\right)={ln}\mid\frac{{x}−\mathrm{1}}{{x}+\mathrm{1}}\mid \\ $$$$\left.\mathrm{1}\right){determine}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculatef}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\int_{−\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{2}}} {f}\left({x}\right){dx}\:. \\ $$

Question Number 62880 Answers: 0 Comments: 1

when f(E^c ) is equal to (f(E))^c

$${when}\:\:{f}\left({E}^{{c}} \right)\:{is}\:{equal}\:{to}\:\left({f}\left({E}\right)\right)^{{c}} \\ $$

Question Number 62879 Answers: 1 Comments: 0

calculate min Σ_(0≤i≤n and 0≤j≤n) (i+j)

$${calculate}\:{min}\:\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\left({i}+{j}\right) \\ $$

Question Number 62878 Answers: 1 Comments: 0

calculate min Σ_(0≤i≤n and 0≤j≤n) i.j

$${calculate}\:{min}\:\sum_{\mathrm{0}\leqslant{i}\leqslant{n}\:{and}\:\mathrm{0}\leqslant{j}\leqslant{n}} \:\:\:\:{i}.{j} \\ $$

Question Number 62877 Answers: 0 Comments: 1

calculate lim_(n→+∞) Σ_(k=0) ^(2n+1) (n/(n^2 +k))